Saturday, July 26, 2014

How Gravity Makes Things Fall

A new demonstration of gravity, featuring the "Spacetime Stretcher," built mostly out of materials from my garage and the hardware store. More info:

1. As a falling object's path goes increasingly in the space (down) direction, it goes a little bit less in the time direction. Gravity is effectively converting some of its travel through time into travel through space. How much time converts into how much space? It works out to be 186,000 miles of space for every second of time -- that's the speed of light! The equivalence between a little time and a lot of space has a parallel with Einstein's famous equation E = mc^2, where a little mass is equivalent to a lot of energy -- also with the speed of light c as the conversion factor, only squared. It's amazing how all these physics concepts fit together.

2. An object moving up or down at the speed of light, such as a photon, follows a vertical path on our graph. If we could warp the Spacetime Stretcher as much as we wanted, we could make the time axis curve around and re-intersect with this vertical line. That would be a black hole: Even a photon moving straight up would get "warped back" to the place where it started.

3. Spacetime warping is usually depicted as going into a higher dimension -- in this case, bending toward or away from the camera. But such a device would have been much harder to build. You can think of this model as a two-dimensional "projection" or "shadow" of three-dimensional curvature, i.e. the flattening of a flared-out surface that curls away from the plane of the graph.

4. In addition to mechanically calculating trajectories of objects falling on the Earth, Mars, or Moon, the Spacetime Stretcher (at a zoomed-out calibration scale) can also calculate the length-contraction and time-dilation observed with a rocket traveling close to the speed of light.